AP® Calculus AB-BC

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Moderate

Evaluate Limit Statements, Points on a Graph

APCALC-LGOX5F

Consider the graph of $g(x)$ shown below.

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Which statement about $g(x)$ is NOT true?

A

$g(x)$ is continuous but not differentiable at $x=a$.

B

$\lim \limits_{x \to a^+} \cfrac{g(x)-g(a)}{x-a} \neq \lim \limits_{x \to a^-} \cfrac{g(x)-g(a)}{x-a}$.

C

$\lim \limits_{h \to 0} \cfrac{g(b+h)-g(b)}{h}=0$.

D

$g’(x)$ exists at $x=c$.